PROBABILITY SAMPLING TECHNIQUES

Outcome 1:Use a variety of sources for the collection of data, both primary

and secondary

1.2 Describe and justify the survey methodology and

frame used

1.6PROBABILITY SAMPLING TECHNIQUES

SAMPLING

PROBABILITY SAMPLING TECHNIQUES

1. Simple Random Sampling (SRS)

• Assure that each element in the population has an equal chance of being selected.• Selection is free from bias• Can calculate the probability – sample size (n) and population size (N)

Therefore, the probability is = n/N• can be done with or without replacement

Possibility of selecting the same item as a

sample twice

More convenience, more precise

result


• Several ways of selecting a simple random sample:

Humans have long practiced various forms of random selection, such as picking a name out of a hat, or choosing the short straw.i. Lottery draw: The name or

identifying number of each item in the population is recorded on a slip of paper and placed in a box - shuffled – randomly choose required sample size from the box.


Techniques of selecting a simple random sample:

ii. Each item is numbered and a table of random numbers is used to select the members of the sample.

iii. There are many software programs, such as MINITAB and Excel that have routines that will randomly select a given number of items from the population.

Example 1: Simple Random Sampling (SRS)Imagine that you own a movie theatre and you are offering a special horror movie film festival next month. To decide which horror movies to show, you survey moviegoers asking them which of the listed movies are their favourites. To create the list of movies needed for your survey, you decide to sample 100 of the 1,000 best horror movies of all time.a. Horror movie population is divided evenly into

classic movies (those filmed in or before 1969) and modern movies (those filmed in or later than 1970).

b. Write out all of the movie titles on slips of paper and place them in an empty box.

c. Draw out 100 titles and you will have your sample.

By using this approach, you will have ensured that each movie had an equal chance of selection.

Example 2: Simple Random Sampling (SRS)

In order to get your sample, you;

a.Assign a number from 001 to 500 to each students,b.use a table of randomly generated numbers (RandomNumber Tables)

Suppose your college has 500 students (population) and you need to conduct a short survey on the quality of the food served in the cafeteria. You decide that a sample of 70 students (sample) should be sufficient for your purposes.


No. Students Name

ID Gender

001 Aaaab F

002 Aabbb F

003 Abbbc M

004 Baaaa M

005 Bbbaa M

006 Bcaab F

… …

… …

499 Mmnnr M

500 Zzwrnn M

Eg: solution

3 digits

c. Randomly pick a starting point in the table, and look at

the random number appear there.d. (In this case) The data run into three digits

(500), the random number would need to contain three

digits as well.e. Ignore all random numbers greater than 500

because they do not correspond to any of the students

in the college.f. Remember !! Sample is without replacement,

so if the number recurs, skip over it and use the next

random number.g. The first 70 different numbers between 001 to

500 make up your sample.


Unit 6: Business Decision MakingPrepared by: Mdm. Nor Azian Abu Asan

Dept. of Maths & Stats


Random Number Tables

• Selection of units is based on sample interval, k starting from a determined point, where k = N/n

ii. First sample drawn between 1 and k randomly (determine point/ the random start ).

iii.Afterwards, every k th must be drawn until the total sample has been drawn.

2. Systematic (Random) Sampling• there is a gap, or interval, between each

selected unit in the sample.

i. Number the units on your frame from 1 to N and the population are arranged in some way

Steps:

Example 3: Systematic (Random) Sampling • Using the same survey problem from Example (1): SRS a. Number the

units on your frame (students) from 1 to N (population). In this case, N = 500.

b. Determine the sample interval, k = N/n, k = 500/70,

k = 7.1, k = 8 (rounding up) .

No. Students Name

ID Gender

001 Aaaab F

002 Aabbb F

003 Abbbc M

… … …

008 Dddbb M

… F

016 Fffaaa M

… … …

499 Mmnnr M

500 Zzwrnn M

Example 3: Systematic (Random) Sampling

**You will need to select one unit (student) of every 8th units to end up with a total of 70 students as your sample.

c. Select a number between 1 and 8 at random (random start)

No. Students Name

ID Gender

001 Aaaab F

002 Aabbb F

003 Abbbc M

… … …

008 Dddbb M

… F

016 Fffaaa M

… … …

499 Mmnnr M

500 Zzwrnn M

Sele

ct 1

of

8

rand

om

ly

Example 3: Systematic (Random) Sampling Example, if you choose number 5, then the 5th student on your frame would be the first unit included in your sample.

Select every kth unit after that first number. Eg: 5 (the random start), 13 (5+8), 21 (13+8), 29 (21+8),… up to 500,(where the total sample needed are obtain).

No. Students Name

ID Gender

001 Aaaab F

002 Aabbb F

… … …

005 Ddaac F

… … …

008 Dddbb M

… … …

013 Eaaaf F

… … …

021 Hhaat F

… … …

500 Zzwrnn M

1st

2nd3rd

• The market researcher might select every 5th person who enters a particular store, after selecting the first person at random.

Example 4: Systematic (Random) Sampling

• The surveyor may interview the occupants of every fifth house on a street, after randomly selecting one of the first five houses.

Systematic (Random) Sampling

Suppose you run a large grocery store and have a list of the employees in each section.

• The grocery store is divided into the following 10 sections: deli counter, bakery, cashiers, stock, meat counter, produce, pharmacy, photo shop, flower shop and dry cleaning.

• Each section has 10 employees, including a manager (making 100 employees in total).

• Your list is ordered by section, with the manager listed first and then, the other employees by descending order of seniority.


If you use a systematic sampling approach and your sampling interval, k = 10, then you could end up selecting only managers or the newest employees in each section.

Possible error:This type of sample would not give you a complete or appropriate picture of your employees' thoughts.

You wanted to survey your employees about their thoughts on their work environment.

Would you used Systematic Sampling Techniques?

• A population is divided into homogenous, mutually exclusive subgroups, called strata and a sample is selected from each stratum.

• Goal: To guarantee that all groups in the population are

adequately represented.• Within stratum - uniformity (homogenous), Between strata – differences (heterogeneous).

3. Stratified (Random) Sampling

• Number of sample from each stratum – select randomly = no. of element in the stratum x no. samples no. of population require

• can be stratified by any variable that is available e.g Gender (Male & Female), edu. Level (SPM, diploma, 1st degree,…),etc.

Stratified (Random) Sampling

Using the same survey problem from Example (1): SRS

If you were select a simple random sample of 70 students from the frame, you might be end up with just a little over 350 female students in your college, since they account for more than half of a % of the whole college students population).

Example 5: Stratified (Random) Sampling

a. Stratifying the population by gender. (Male and Female)

b. Calculate the exact sample size from each strata;

Male = (150/500)*70 = 21 male students Female = (350/500)*70 = 49 female students

Give the total sample = 21 + 49 = 70 students

Using the same survey problem from Example (1): SRS

c.Each units (students) from each strata will be numbered, then the sample from each strata will be selected at random (as in SRS).



No. Students Name

ID Gender

001 Aaaa F

002 Bbbb F

003 Cccc F

004 Dddd F

005 Eeee F

006 Ffff F

… … F

350 Yyyy F

No. Students

Name

ID Gender

001 Aabb M

002 Bbcc M

003 Ccdd M

004 Ddee M

005 Eeff M

006 Ffgg M

… M

150 Zzzz M

Strata (by Gender)

Female = 49

Male = 21

Extra Easy Sudoku Puzzle #3

http://puzzles.about.com/od/sudokupuzzles/qt/EESuDokuSol03.htm

• To reduce the cost of sampling a population scattered over a large geographic area.

• To gather data quickly and cheaply at the expense of possible over – or under representing certain groups of people.

4. Cluster (Random) Sampling

- By the luck of the draw you will wind up with respondents who come from all over the state

Cluster (Random) Sampling

Steps:

• divides the population into groups or clusters- Within cluster- differences (heterogeneous)

- Between cluster– uniformity (homogenous)

• select clusters at random - all units within selected clusters are included

in the sample- No units from non-selected clusters are included in the sample

Imagine that the municipal council of Perak Tengah wants to investigate the use of health care services by residents.

a. Council requests for electoral subdivision maps that

identify and label each area block.

b. From this maps, the council creates a list of all area

blocks (e.g: Bota, Parit, Kg.Gajah, Manong,…). This area will serve as the survey sampling frame.

c. Every household in that area belongs to a area block.

d. Each area block represents a cluster of households.

Example 5: Cluster (Random) Sampling

e. Council randomly picks a number of area blocks (cluster)

using SRS approach.

c. List all households in the selected area blocks; these

households make up the survey sample.

Example 5: Cluster (Random) Sampling

• Combination of all the methods described above.

• Involves selecting a sample in at least two stages.

e.g: i. Stage 1: Stratified Sampling Stage 2: Systematic Sampling

e.g: ii. Stage 1: Cluster Sampling Stage 2: Stratified Sampling

Stage 3: Simple Random Sampling

5. Multi-stage Sampling

Advantages & Disadvantages

Sampling Techniques

Advantages Disadvantages

Simple Random Sampling

i. Easiest method & commonly used.ii. Not require any additional info. on the frame (such as gender, geographical area etc), other than complete list of members along with contact info.iii. Analysis of data is reasonably easy and has a sound mathematical basis.

i. Make no use of auxiliary info. ii. Can be expensive and unfeasible for large

population (to identified

and reach) or if the

personal interview required.

iii. not be representative of the whole population

Sampling Techniques



i. Easier to draw, without mistakes.ii. More precise than SRS as more evenly spread over population.

i. If list has periodic arrangement then sample collected may not be an accurate representation of the entire population.


Sampling Techniques


Stratified (Random) Sampling

i. Ensure an adequate sample size for subgroups in the population of interest.ii. Almost certainly produce a gain in precision in the estimates of the whole population, because a heterogeneous population is split into fairly homogeneous strata.

i. Problem if strata

not clearly defined.

ii. Analysis is (or can be) quite

complicated.


Sampling Techniques


Cluster Sampling

i. Reduced field costsii. Applicable where no complete list of units is available (special lists only need be formed for clusters).

i. Clusters may not be representative of whole population but may be too alike.

ii. Analysis more complicated

than for SRS.


PROBABILITY SAMPLING TECHNIQUES

Education